Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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          <p>
            <s xml:id="echoid-s10400" xml:space="preserve">
              <pb o="401" file="0421" n="421" rhead="LIBER V."/>
            rum hyperbol arum, FAD, EVC, ad omnia quadrata, TN, dem-
              <lb/>
            ptis omnibus quadratis oppoſitarum hyperbolarum, TAY, MVN,
              <lb/>
            quod, &</s>
            <s xml:id="echoid-s10401" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10402" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div947" type="section" level="1" n="565">
          <head xml:id="echoid-head590" xml:space="preserve">THEOREMA XXIII. PROPOS. XXIV.</head>
          <p>
            <s xml:id="echoid-s10403" xml:space="preserve">IN eadem antecedentis figura, regula ſumpta, DC, oſtẽ-
              <lb/>
            demus omnia quad. </s>
            <s xml:id="echoid-s10404" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s10405" xml:space="preserve">FADCVE, ad omnia quadra-
              <lb/>
            ta figuræ, TAYNVM, eſſe vt paralle lepipedum ſub, XL, & </s>
            <s xml:id="echoid-s10406" xml:space="preserve">
              <lb/>
            quadrato, RZ, cum duplo quadrati, AV, ad parallelepipe-
              <lb/>
            dum ſub, HG, & </s>
            <s xml:id="echoid-s10407" xml:space="preserve">quadrato, BS, cum duplo quadrati, AV.</s>
            <s xml:id="echoid-s10408" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10409" xml:space="preserve">Omnia namque quadrata figuræ, FADCVE, ad omnia quadra-
              <lb/>
            ta figuræ, TAYNVM, habent rationem compoſitam ex ea, quam
              <lb/>
            habent omnia quadrata figuræ, FADCVE, ad omnia quadrata,
              <lb/>
            FC, .</s>
            <s xml:id="echoid-s10410" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10411" xml:space="preserve">ex ratione quadrati, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10412" xml:space="preserve">quadrati, KI, (quæ ſit
              <lb/>
            portio, DC, capta inter aſymptotos, qui ſint, PI, KQ, ducti per,
              <lb/>
              <note position="right" xlink:label="note-0421-01" xlink:href="note-0421-01a" xml:space="preserve">21. huius.</note>
            O, ſecantes, YN, in, &</s>
            <s xml:id="echoid-s10413" xml:space="preserve">, ℟, FE, in, P, Q, &</s>
            <s xml:id="echoid-s10414" xml:space="preserve">, TM, in, Ω, Π) ad
              <lb/>
            quadratum, DC, & </s>
            <s xml:id="echoid-s10415" xml:space="preserve">ex ratione omnium quadratorum, FC, ad om-
              <lb/>
            nia quadrata, TN, quæ eſt compoſita ex ea, quam habet quadra-
              <lb/>
            tum, DC, ad quadratum, YN, & </s>
            <s xml:id="echoid-s10416" xml:space="preserve">ex ea, quam habet, EC, ad, MN,
              <lb/>
              <note position="right" xlink:label="note-0421-02" xlink:href="note-0421-02a" xml:space="preserve">11. l. 2.</note>
            & </s>
            <s xml:id="echoid-s10417" xml:space="preserve">tandem ex ratione omnium quadratorum, TN, ad omnia qua-
              <lb/>
            drata figuræ, TAYNVM, .</s>
            <s xml:id="echoid-s10418" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10419" xml:space="preserve">ex ratione quadrati, YN, ad quadra-
              <lb/>
            tum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10420" xml:space="preserve">quadrati, & </s>
            <s xml:id="echoid-s10421" xml:space="preserve">℟, porrò ex his rationibus compo-
              <lb/>
            nentibus ea, quam habet quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10422" xml:space="preserve">quadrati, KI, ad
              <lb/>
              <note position="right" xlink:label="note-0421-03" xlink:href="note-0421-03a" xml:space="preserve">21. huius</note>
            quadratum, DC, item quadratum, DC, ad quadratum, YN, & </s>
            <s xml:id="echoid-s10423" xml:space="preserve">
              <lb/>
            quadratum, YN, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10424" xml:space="preserve">quadrati, & </s>
            <s xml:id="echoid-s10425" xml:space="preserve">℟, com-
              <lb/>
            ponunt rationem quadrati, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10426" xml:space="preserve">quadrati, KI, ad quadra-
              <lb/>
            tum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10427" xml:space="preserve">quadrati, & </s>
            <s xml:id="echoid-s10428" xml:space="preserve">℟, vel triplicatis terminis, compo-
              <lb/>
            nunt rationem trium quadratorum, AV, cum quadrato, KI, ad
              <lb/>
            tria quadrata, AV, cum quadrato, & </s>
            <s xml:id="echoid-s10429" xml:space="preserve">℟, vel componunt rationem
              <lb/>
              <note position="right" xlink:label="note-0421-04" xlink:href="note-0421-04a" xml:space="preserve">Def. 12.
                <lb/>
              l. 1.</note>
            trium quadratorum, OV, cum quadrato, LI, ad tria quadrata, O
              <lb/>
            V, cum quadrato, G ℟; </s>
            <s xml:id="echoid-s10430" xml:space="preserve">quadratum autem, LI, eſt æquale rectan-
              <lb/>
            gulo, OVZ, bis cum quadrato, VZ, & </s>
            <s xml:id="echoid-s10431" xml:space="preserve">quadratum, G℟, æquale
              <lb/>
            rectangulo, OVZ, bis cum quadrato, VS; </s>
            <s xml:id="echoid-s10432" xml:space="preserve">nam rectangulum, KC
              <lb/>
            I, ex prop. </s>
            <s xml:id="echoid-s10433" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10434" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s10435" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10436" xml:space="preserve">Conicorum æquatur quadrato, OV, & </s>
            <s xml:id="echoid-s10437" xml:space="preserve">idẽ
              <lb/>
            rectangulum, KCI, cum quadrato, IL, æquatur quadrato. </s>
            <s xml:id="echoid-s10438" xml:space="preserve">LC, vel
              <lb/>
            quadrato, OZ, vnde quadratum, LI, remanet æquale rectangulo
              <lb/>
            ſub, OVZ, bis cum quadrato, VZ; </s>
            <s xml:id="echoid-s10439" xml:space="preserve">& </s>
            <s xml:id="echoid-s10440" xml:space="preserve">ſic etiam quadratum, G℟,
              <lb/>
            concludetur æquale eſſe rectangulo bis ſub, OVS, cum </s>
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